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Dielectric Collimatorsfor the CLIC Beam Delivery System?

First ideas from studies for the LHC collimators

E. Métral, A. Grudiev, G. Rumolo, B. Salvant (also at EPFL, Lausanne), R. TomàsCERN, Geneva

Many thanks for their help and advice to

E. Adli, R. Calaga, F. Caspers, A. d’Elia, A. Latina, F. Roncarolo, D. Schulte, C. Simon

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Agenda

• Context

• Why consider dielectrics for LHC collimation?– Idea– Impedance code (ReWall)– Results and recommendations

• Coarse extrapolations to the case of the CLIC bunch as anintroduction to future work– Analytical estimates– Electromagnetic simulations (CST Particle Studio)

• Perspectives

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• BDS Collimation System needed for background reduction and machine protection

• However, collimators may generate strong wakefields and affect the beam qualityluminosity limitation

Context: CLIC BDS collimation system

- CLIC collimation system review: optics issuesand wakefield effects, J. Resta Lopez, 15/01/2009

- Tracking with Collimator Wake-Fields through the CLIC BDS,A.Latina, G.Rumolo, D.Schulte, 19/05/2006

spoiler absorber

Courtesy: J. Resta Lopez

beam~0.1 mm

Courtesy: J. Resta Lopez

Simulated loss of CLIC luminosityas a function of beam initial vertical offset

Need to minimize the BDS collimation wakefield

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Context: Recent ideas for LHC collimation

• Concern for the high impedance of the collimators, especially at low frequencies

• However, impedance does not increase steadily at low frequencies

• As a consequence, materials with low conductivities could also be consideredIn particular, dielectric materials offer a wide range of electrical, mechanicaland thermal properties.may be an opportunity to find an optimized solution for the phase IIcollimation system

Classical thick wall theory“New” formalisms

(Zotter/Metral, Burov/Lebedev)

Example:Real part of impedance of a cylindricalcollimator (infinitely thick copper layer)(aperture radius = 0.1 mm, length 60 cm)

Comparison between Laboratory Measurements, Simulations and Analytical Predictions of the Transverse WallImpedance at Low Frequencies, F. Roncarolo et al, EPAC’08 and submitted to PRST/AB .

Question : would it be a good idea to also consider dielectric materialsfor the CLIC BDS collimation system?

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Agenda

• Context

• Why consider dielectrics for LHC collimation?– Idea– Impedance code (ReWall)– Results and recommendations

• Coarse extrapolations to the case of the CLIC bunch as anintroduction to future work– Analytical estimates– Electromagnetic simulations (CST Particle Studio)

• Perspectives

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Why consider dielectrics for LHC collimation?idea

• For circular accelerators, the impact of the transverse impedance Ztrans( ) on the beambehaviour depends on the bunch power spectrum h( ):

krmsk

krmskktrans

rmseff

h

hZZ

,

,(simplified formula for the sake of understandingsee Sacherer’s formula for a more complete descriptionincluding chromaticity and bunched beam modes)

Real impedance Re(Ztrans)

frequency

Bunch power spectrum h

frequency

(Gaussian bunch of rms length rms)2

, rmseh rmsk

Bunch power spectrum h

LHC CLIC

Impedance frequency range“seen” by the bunch

frequency

LHC 1 GHzCLIC a few THz

Frequency range of impedance“seen” by the bunch:

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Why consider dielectrics for LHC collimation?idea

• Classical impedance theoryprimary concern for LHC collimators was the high impedance at low frequency (10 kHz)

and the resulting coupled bunch instabilities.

• “New” theories, the impedance is no longer monotonous.higher conductivity shifts the peak to lower frequencies

Impedance frequency rangeseen by the bunch

frequencyfrequency

Real impedance Re(Ztrans)

Bunch power spectrum h

Re(Z), h Re(Z), h

Classical “thick wall”impedance theory

“New” formalisms(Zotter/Metral, Burov/Lebedev)

In this case, the diverging impedanceat low frequency is more critical

In this case, it really depends on the frequencyand bandwidth of the impedance peak

>

Idea: can we shift the impedance peak outside of the LHC bunch spectrum?And reduce the impedance that interacts with the beam

>

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Agenda

• Context

• Why consider dielectrics for LHC collimation?– Idea– Impedance code (ReWall)– Results and recommendations

• Coarse extrapolations to the case of the CLIC bunch as anintroduction to future work– Analytical estimates– Electromagnetic simulations (CST Particle Studio)

• Perspectives

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Why consider dielectrics for LHC collimation?impedance model (ReWall)

• We wrote an analytical code which is able to compute the beam coupling impedance of a cylindricalstructure composed of various layers of different materials (no restriction on the material parameters).

• This impedance code solves Maxwell equations and uses field matching at al all material boundaries tofind the total longitudinal and transverse impedance of the structure (Zotter/Metral formalism).

• Impedance of a round collimator can be calculated, and analytical coefficients (Yokoya/Laslett) areapplied to obtain the impedance of a flat collimator.

• This code makes no approximation, is numerically very demanding, and the number of layers can notbe too high if no simplification is to be made.

• The wakes can be computed from the impedance via DFT (not a trivial step).

ceramicgraphitecopper

Example of impedance result

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Agenda

• Context

• Why consider dielectrics for LHC collimation?– Idea– Impedance code (ReWall)– Results and recommendations

• Coarse extrapolations to the case of the CLIC bunch as anintroduction to future work– Analytical estimates– Electromagnetic simulations (CST Particle Studio)

• Perspectives

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STUDIES ONGOING FOR A CERAMIC COLLIMATOR (1/10)

5rScan in resistivity from 10-6 to 1020 m and

peakst1f

/1peaknd2f

ANALYTICAL PREDICTIONS

2 mm

+

Higher resistivity leads to real part peak shifts to very high frequencies (for LHC…)increase of the imaginary part at high frequencies

r

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TRANSVERSE IMPEDANCE

Ceramic+vacuum

Graphite+vacuum

Copper+vacuum

copper coating+ ceramic+ vacuum

dielectric alone leads to higher real and imaginary impedance above 10 MHz not goodhowever copper coated ceramic may be tuned to lead to lower impedance, depending on theceramic and the beam parameters

ceramic2 mm

+

r

2.5 cm

2 mm

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Why consider dielectrics for LHC collimation?

• In addition, another issue also comes up with dielectrics:If a perfect conductor is placed behind the dielectric (instead of vacuum),

many resonances appear due to constructive interference in the dielectric(multiple reflections at metal/dielectric and dielectric/air interfaces)

(Perfect Conductor)

A copper coating would also prevent these resonances from happening

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And for CLIC?

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Agenda

• Context

• Why consider dielectrics for LHC collimation?– Idea– Impedance code (ReWall)– Results and recommendations

• Coarse extrapolations to the case of the CLIC bunch as anintroduction to future work– Analytical estimates– Electromagnetic simulations (CST Particle Studio)

• Perspectives

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Impedance of the CLIC BDS collimator

• 2 contributors:– Geometric impedance (taper)– Resistive impedance (collimator is very close to the beam)

What are their relative weight?

• The resistive part can be estimated by our analytical code

• Time domain electromagnetic simulations can help calculating wake fields forthe geometric part (ABCI, CST, GdfidL, Xwake…)

• 2 challenges:1) What is our material??? Conductivity, permittivity and their frequency dependence?

Need for precise description.

2) Micrometer bunch in a meter long structure… numerically challengingGdfidL moving mesh or 2D code?

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Agenda

• Context

• Why consider dielectrics for LHC collimation?– Idea– Impedance code (ReWall)– Results and recommendations

• Coarse extrapolations to the case of the CLIC bunch as anintroduction to future work– Analytical estimates– Electromagnetic simulations (CST Particle Studio)

• Perspectives

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Analytical estimates: Resistive wall impedance

• CLIC BDS collimator:– Length 60 cm, inner radius 0.1 mm, = 3 106

0.1 mm

+

r

0.1 mm

+

r

0.1 mm

8 mm

r

Copperresistivity = 1.7 10-8 .mrelaxation time =2.7 10-14 s)

Graphiteresistivity = 1 10-5 .mrelaxation time =8 10-13 s)

Dielectric + copperdielectric resistivity = 1012 .mDielectric permittivity r = 5

+

Frequency in Hz

Zoom

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Now let’s take the DFT to obtain the wake!

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Analytical estimates: Resistive wall wake• CLIC BDS collimator:

– Length 60 cm, inner radius 0.1 mm, = 3 106

0.1 mm

+

r

0.1 mm

+

r

0.1 mm

8 mm

r

Copperresistivity = 1.7 10-8 .mrelaxation time =2.7 10-14 s)

Graphiteresistivity = 1 10-5 .mrelaxation time =8 10-13 s)

+

Dielectric + copperdielectric resistivity = 1012 .mDielectric permittivity r = 5

This dielectric example is worse than copperGraphite is probably not a good ideaHigh frequency properties are essential!!!

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Agenda

• Context

• Why consider dielectrics for LHC collimation?– Idea– Impedance code (ReWall)– Results and recommendations

• Coarse extrapolations to the case of the CLIC bunch as anintroduction to future work– Analytical estimates– Electromagnetic simulations (CST Particle Studio)

• Perspectives

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Disclaimer• The following simulations are just first attempts on a much smaller collimator structure.

• Very small rms bunch length (~0.1 ps) compared to collimator size (1m*16mm*16mm)very small mesh size required in a very large volumenot achievable with CST Particle Studio (Could be achieved with GdfidL with a

moving mesh focused on obtaining the short range wake)

CLIC BDS Collimator plan Simulated geometry

2.5mminstead of8 mm

5 mminstead of60 cm

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Vertical Electric field simulated by particle studio

Graphite

Copper

Dielectric

Angle of the shock waveagrees with cerenkov effect

rn11sin

Less reflections with a dielectric taper?

No relaxation time

No relaxation time

r=5=1 m

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Agenda

• Context

• Why consider dielectrics for LHC collimation?– Idea– Impedance code (ReWall)– Results and recommendations

• Coarse extrapolations to the case of the CLIC bunch as anintroduction to future work– Analytical estimates– Electromagnetic simulations (CST Particle Studio)

• Perspectives

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Conclusions

• The reasons that lead us to consider dielectrics as low impedance materialsfor LHC collimations may not be relevant for CLIC.

• However, fine tuning of the material properties is still possible to try andminimize the wakes

• With the examples studied, it seems the geometric impedance of the tapercould be smaller for a dielectric than for copper (to be checked with GdfidL),but the resistive wall impedance will be larger.

• These wakes could be input into PLACET (or Headtail?) for more precisebeam dynamics simulations.

• Both time domain simulations and analytical computations are demandingfor CLIC BDS collimator parameters. An idea would be to use a 2D codesuch as ABCI, Mafia or Xwake to gain in simplicity.

• High frequency specifications and measurement of the materials seem to beessential.

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Many thanks for your attention!